MA 2611
D ’07
Quiz 1a Solution
1. (6 points) A gage R&R study is conducted to assess the process for measuring the
diameter of a wayfinding tool extender. The study uses three operators each measuring
the diameter of the same wayfinding tool extender multiple times using the same gauge.
Figure 1 shows three stratified plots that might result. Match each plot to the correct
variation measures:
a. Within sum of squares: 26150; Between sum of squares: 120.
b. Within sum of squares: 13075; Between sum of squares: 13727.
c. Within sum of squares:
7180; Between sum of squares: 19682.
1
2
3
O p e r a t o r
20
40
60
80
100
120
y
1
2
3
O p e r a t o r
50
100
150
y
1
2
3
O p e r a t o r
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100
150
y
s e t
=
1
s e t
=
2
s e t
=
3
Figure 1
Set=1:_b__
Set=2:_a__
Set=3:_c__
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2. (2 points) What percentage of the variation in Set 1 of question 1 is due to
reproducibility?
Solution: The variation due to reproducibility is measured by between variation, so the
percentage is (100)(13727/[13727+13075])=51.2%
3. (2 points) What should have been checked before summarizing the Gage R&R results
using a stratified plot of the type shown in Figure 1?
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 Spring '08
 Petrucelli
 Mean, Gage R&R, home runs, tool extender

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